Visible to the public Compositional Abstraction for Networks of Control Systems: A Dissipativity Approach

TitleCompositional Abstraction for Networks of Control Systems: A Dissipativity Approach
Publication TypeJournal Article
Year of Publication2018
AuthorsZamani, Majid, Arcak, Murat
JournalIEEE Transactions on Control of Network Systems
Date PublishedSept. 2018
KeywordsAerospace electronics, Approximate abstractions, compositional abstraction, compositional scheme, compositionality, control nonlinearities, control system networks, control system synthesis, controller design process, dissipativity, dissipativity approach, dissipativity-type compositional reasoning, dissipativity-type properties, interconnection matrix, Large-scale systems, linear control systems, Linear systems, linear temporal logic specification, Matrices, matrix algebra, networks of control systems, nonlinear control systems, process control, pubcrawl, simulation functions, storage functions, Symmetric matrices, system nonlinearities, temporal logic, Trajectory

In this paper, we propose a compositional scheme for the construction of abstractions for networks of control systems by using the interconnection matrix and joint dissipativity-type properties of subsystems and their abstractions. In the proposed framework, the abstraction, itself a control system (possibly with a lower dimension), can be used as a substitution of the original system in the controller design process. Moreover, we provide a procedure for constructing abstractions of a class of nonlinear control systems by using the bounds on the slope of system nonlinearities. We illustrate the proposed results on a network of linear control systems by constructing its abstraction in a compositional way without requiring any condition on the number or gains of the subsystems. We use the abstraction as a substitute to synthesize a controller enforcing a certain linear temporal logic specification. This example particularly elucidates the effectiveness of dissipativity-type compositional reasoning for large-scale systems.

Citation Keyzamani_compositional_2018